)) Use algebra tiles to find \( \left(x^{2}+5 x\right)+\left(8 x^{2}+8 x+3\right) \)

Certainly! Let's use **algebra tiles** to add the two polynomials: \[ \left(x^{2} + 5x\right) + \left(8x^{2} + 8x + 3\right) \] **Algebra Tiles Overview:** - **\( x^2 \) tile**: Represents the quadratic term. - **\( x \) tile**: Represents the linear term. - **\( 1 \) tile**: Represents the constant term. **Step 1: Represent Each Polynomial with Algebra Tiles** 1. **First Polynomial: \( x^{2} + 5x \)** - **\( x^2 \) tiles**: 1 - **\( x \) tiles**: 5 - **\( 1 \) tiles**: 0  2. **Second Polynomial: \( 8x^{2} + 8x + 3 \)** - **\( x^2 \) tiles**: 8 - **\( x \) tiles**: 8 - **\( 1 \) tiles**: 3  **Step 2: Combine the Tiles** Add the corresponding tiles from both polynomials: - **Total \( x^2 \) tiles**: \(1 + 8 = 9\) - **Total \( x \) tiles**: \(5 + 8 = 13\) - **Total \( 1 \) tiles**: \(0 + 3 = 3\)  **Step 3: Write the Resulting Polynomial** Combine the totals to form the final polynomial: \[ 9x^{2} + 13x + 3 \] **Final Answer:** \[ (x^{2} + 5x) + (8x^{2} + 8x + 3) = 9x^{2} + 13x + 3 \] **Visualization Summary:** 1. **First Polynomial:** - \( x^2 \) tile × 1 - \( x \) tile × 5 2. **Second Polynomial:** - \( x^2 \) tile × 8 - \( x \) tile × 8 - \( 1 \) tile × 3 3. **Combined:** - \( x^2 \) tile × 9 - \( x \) tile × 13 - \( 1 \) tile × 3 By organizing and combining the algebra tiles, we systematically add like terms to arrive at the simplified polynomial.